﻿ Buydown

# Buydown

Discussion:

The market value of a Buydown is the present value of the difference between the amount of the two monthly (or annual)  payments.  The monthly payment is an annuity so columns 5 and 6 of the compound interest tables are used in this problem.

Present value of a buydown = PV of [Payment #1 minus Payment #2]

Mortgage Problem #3:

Jane is offered a 20 year loan at a 10% rate.  The mortgage company will allow an 8% rate for the first 4 years if she pays 50% of the market value of the buydown in advance.  If Jane borrows \$100,000 and accepts the buydown offer, how much will she have to pay for the buydown.

Solution:

 1 Payment = Mortgage Constant (column 6) x Original Loan Amount (See Problem #1)
 2 Payment @10% = 0.00965022 x \$100,000 = \$965.02
 3 Payment @8% = 0.00836440 x \$100,000 = \$836.44
 4 Difference in payments = \$965.02 - \$836.44 = \$128.58
 5 Present Value of a \$128.58 annuity @10 for 4 years = 0.31547080 x \$128.58 = \$5,070
 6 \$5,070 x 50% = \$2,435 is Jane's cost of the buydown